In the latest data release from the Fermi Gamma-ray Space Telescope (the 4th Fermi LAT 14 yr Catalog, or 4FGL), more than 50% of the Galactic sources are yet to be identified. We observed 13 unidentified Fermi LAT sources with the Chandra X-Ray Observatory to explore their nature. We report the results of the classification of X-ray sources in the fields of these γ-ray sources and discuss the implications for their nature. We use multiwavelength (MW) data for a machine-learning classification, accompanied by a more detailed spectral/variability analysis for brighter sources. Eight 4FGL sources have γ-ray pulsars within their position error ellipses. We consider three of these pulsars (PSR J1906+0722, PSR J1105–6037, and PSR J1358–6025) to be detected in X-rays, while PSR J1203–6242 shows a hint of X-ray emission. Within the positional uncertainties of three of the 4FGL sources, we detect X-ray sources that may be yet unknown pulsars, depending on the MW association. In addition to point sources, we discovered two extended sources, one of which is likely to be a bow-shock pulsar-wind nebula associated with PSR J1358–6025. Finally, we classify other X-ray sources detected in these observations and report the most interesting classifications.
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